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Book Synopsis
Mathematical models involving evolutionary partial differential equations (PDEs) as well as ordinary differential equations (ODEs) arise in diverse applications such as fluid flow, image processing and computer vision, physics-based animation, mechanical systems, relativity, earth sciences, and mathematical finance. This text develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems. Both PDEs and ODEs are discussed from a unified view. The author emphasises finite difference and finite volume methods, specifically their principled derivation, stability, accuracy, efficient implementation, and practical performance in various fields of science and engineering. Smooth and non-smooth solutions for hyperbolic PDEs, parabolic-type PDEs, and initial value ODEs are treated, and a practical introduction to geometric integration methods is also included. The author bridges theory and practice by developing algorithms, concepts, and analysis fr

Numerical Methods for Evolutionary Differential

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    A Paperback by Uri M. Ascher

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      Publisher: Society for Industrial and Applied Mathematics
      Publication Date: Publication Date: 9/4/2008
      ISBN13: 9780898716528, 978-0898716528
      ISBN10: 0898716527

      Description

      Book Synopsis
      Mathematical models involving evolutionary partial differential equations (PDEs) as well as ordinary differential equations (ODEs) arise in diverse applications such as fluid flow, image processing and computer vision, physics-based animation, mechanical systems, relativity, earth sciences, and mathematical finance. This text develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems. Both PDEs and ODEs are discussed from a unified view. The author emphasises finite difference and finite volume methods, specifically their principled derivation, stability, accuracy, efficient implementation, and practical performance in various fields of science and engineering. Smooth and non-smooth solutions for hyperbolic PDEs, parabolic-type PDEs, and initial value ODEs are treated, and a practical introduction to geometric integration methods is also included. The author bridges theory and practice by developing algorithms, concepts, and analysis fr

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